Sparse Matrix Memory Allocation via Symbolic Hash Tables
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for sparse matrix-matrix multiplication struggle to accurately predict the number of non-zero elements in the output matrix, leading to inefficient memory allocation and potential memory waste or excessive dynamic reallocation.
Innovation Solution
A method that computes floating-point multiplication operations and estimates the compression ratio for each row of the output matrix using sampled rows from both sparse matrices, constructs hash tables to determine actual non-zero elements, and allocates memory space based on these calculations, ensuring accurate memory allocation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If memory space is allocated based on predicted non-zero elements, then memory allocation efficiency is improved, but prediction accuracy deteriorates leading to memory waste or excessive reallocation
Solution Approach 1:
The patent performs symbolic computation before numerical multiplication to predict the exact number of non-zero elements in the output matrix. This preliminary action provides accurate memory allocation information before the actual computation, resolving the contradiction between allocation efficiency and prediction accuracy.
Solution Approach 2:
The patent introduces hash tables as an intermediary data structure to count non-zero elements during symbolic computation. The hash tables map column indices to row indices, enabling accurate counting of non-zero elements without performing full numerical multiplication, thus achieving both efficiency and accuracy.
2Quantity of substance
If compact data structure is used for sparse matrices, then memory storage efficiency is improved, but memory allocation complexity worsens due to difficulty in predicting output size
Solution Approach 1:
The patent performs symbolic computation to predict the exact number of non-zero elements before numerical multiplication. This preliminary action simplifies memory allocation for compact data structures by providing accurate size information in advance, reducing allocation complexity while maintaining storage efficiency.
3Measurement precision
If dynamic reallocation is performed during computation, then memory accuracy is improved, but computation time increases due to reallocation overhead
Solution Approach 1:
The patent performs symbolic computation to predict the exact number of non-zero elements before numerical multiplication begins. This allows static memory allocation based on accurate predictions, eliminating the need for dynamic reallocation during computation and avoiding the time overhead associated with reallocation operations.
Data Source
AI summary
This application describes accelerator, computer system, and method for memory allocation in sparse matrix-matrix multiplications (spGEMM). An example method may include: computing a number of floating point multiplication operations (FLOP) to be performed to generate each row in the output matrix; determining an estimated compression ratio based on a plurality of first rows sampled from the first sparse matrix and a plurality of corresponding second rows from the second sparse matrix; determining an estimated number of non-zero data (NNZ) in each row of the to-be-generated output matrix; constructing a plurality of hash tables for the rows in the to-be-generated output matrix based on the estimated NNZ corresponding to each row; performing symbolic computations between the first and second sparse matrices by using the hash tables to determine actual NNZs in the to-be-generated output matrix; and allocating a memory space for the output matrix based on the actual NNZs.